If 1 lies between the roots of the equation 3x2 3 sin αx 2 cos2 α - Maths - Complex Numbers and Quadratic Equations

Question

If 1 lies between the roots of the equation 3x
2 – 3 sin αx – 2
cos2 α = 0 then α lies in the interval

(1) 0 ,   π 2 (2) π 12 ,   π 2 (3) π 6 ,
  5 π 6 (4) π 6 , π 2 ∪ π 2 ,   5 π 6

Neha Sethi · Accepted Answer

Dear student
We have,3x2-3sinax-2cos2a=0If 1 lie between the roots then on substituting  1 in the  above equation it will  give zero
 So , 3-3sina-2cos2a<0⇒3-3sina-2(1-sin2a)<0⇒2sin2a-3sina+1<0⇒sina-12sina-1<0⇒12<sina<1⇒π6<a<5π6
Regards

If 1 lies between the roots of the equation 3x 2 – 3 sin αx – 2 cos2 α = 0 then α lies in the interval (1) 0 , π 2 (2) π 12 , π 2 (3) π 6 , 5 π 6 (4) π 6 , π 2 ∪ π 2 , 5 π 6

If 1 lies between the roots of the equation 3x ² – 3 sin αx – 2 cos² α = 0 then α lies in the interval

(1) $(0, \frac{π}{2})$ (2) $(\frac{π}{12}, \frac{π}{2})$ (3) $(\frac{π}{6}, \frac{5 π}{6})$ (4) $(\frac{π}{6}, \frac{π}{2}) \cup (\frac{π}{2}, \frac{5 π}{6})$